Removing duplicates from an array

I have a file from which I'm reading a Point objects. I put them into an array, and I need to remove any duplicates. I think my code should work, but when I check the elements in the array, duplicates are still there. Can you please provide some feedback on what I'm doing wrong?

p.s. The code to initially fill the array works, the only problem that I have is that the duplicates are not being removed. (Lines 8 to 10)

The Point must be able to be compared if I am not mistaken as the Set/HashSet will not allow duplicates, but it must have some way to tell if one Point object is equal to another Point object in order to work.

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